Your are not alone and since this is my first year I have asked the same question about leaving the univolt plugged in. I did not like the answer I got back, namely vague as to what the univolt should do and what is the best practice.

My manual (1987) implies that the univolt is an intelligent charger and will trickle charge as the batteries reach full charge. Yours obviously doesn't reduce charge enough and I doubt that mine does either.

I have been charging periodically for a day or so and then I have been unplugging for a couple weeks. I have not used the dead kill switch that is available because of the cautionary statement in the manual if you forget it.

I think I will install 1 amp trickle chargers on each battery same as I use on the diesel tractor battery. For $25 you can get one that will turn on and off auto.

When I first got my MH I left it plugged into shore power in my driveway when being stored. Both my delco marine rv batteries fried over a years time, and are sealed so no fluid could be added.
I have since gone to an occasional voltage check, and a charge with a deep cycle 15 amp charger I bought. Seems to be better all the way around, and not a whole lot of hassle.

My A/S has an original Univolt, made by Litton. I have not had any overcharging problems. I check the water in the battery every month or so. Like John HD, I seem to add very little water. If the weather is cool, and the Fantastic Fan doesn't cycle much I shut the Univolt off for a week at a time. I check the voltage with a digital voltmeter, and turn the Univolt back on as needed. Seems to use around 65 KWH per month.

I went with two Optima Gel type batteries AND a responsible charging system (intelli charger with charge wizard) two years ago and haven't had a problem since.
I learned the hard way. Autozone stores thru-out the country used to barricade their stores when they saw me pulling up with my previous Motorhome..3-4 times a year.
It doesn't matter if you keep the water level up, if you boil the batteries.
For MH owners driving with the generator running, this is a valid fact to consider.

The Univolt should not cook the batteries and if it is, there's probably something wrong with the Univolt. Again the output voltage should be between 13.8 and 14.2.

yeah, it shouldn't.....but it does!

my univolt does output between 13.8 and 14.2 volts....all the time, whether it needs to or not. I thought that was the problem: it sends a constant voltage to the battery, regardless of the charge state of the battery, and that this is what'll happen with any charger, if you leave it on for too long. (that is, any charger without the features of the "charge-wizard", that monitors the battery's condition and adjusts itself accordingly).

.... So I have read from the various posts... (unless one goes for a REAL Intellicharger with a battery moniter) ....

The best results are apparently occasionally charging with the Univolt. Since I like the idea of leaving the TT plugged in I am thinking of installing a 110 volt 24 hour timer in line with the charger.

I'm surprised no one has mentioned this idea. I could set it to charge for say one hour a day and still have 110 all the time.

I do monitor with a digital multimeter for accurate voltage and have a specific gravity float to check as well.